184- Mr. Pond on the Changes in the 



slniction, the error thus occasioned will be applied to every 

 star under tlie form of co-latitude, and a star south of the 

 zenith will be moreover affected by the probably opposite 

 flexure due to that point of the instrument on which the star 

 is observed. This in stai's near the equator, or a little to the 

 northward of it, will in our latitude give an error in polar di- 

 stance, amounting to about double the error committed in de- 

 termining the co-latitude. On the contrary, the polar distances 

 of stars north of the zenith, being affected only by the differ- 

 ence of two flexui'es, will be more accurately determined as 

 they approach nearer to the pole, where the errors will wholly 

 vanish. Now, though in the usual mode of employing the 

 Greenwich circle, viz. in measuring directly polar distance, 

 the co-latitude does not become an object of iiujuirj-, j'et any 

 flexure of the circle will produce a system of errors of the same 

 nature as those above pointed out. In instruments, like that 

 of Dublin, which turn in azimuth, and with v.hich the observer 

 has to find the place of all the stars by measuring the double 

 of their zenith distances, if he does not find the same zenith 

 point with different stars (provided the instrument be well di- 

 vided) he may be sure that flexure takes jilace ; but he cannot 

 infer the converse, that flexure does not take place, from his 

 obtaining with all the stars the same error in the line of coUi- 

 mation. For if the flexure be the same on both sides of the 

 zenith, a supjiosition by no means improbable, the observe)- 

 will then have no indication of flexure by the usual method of 

 determining the error of coUimation by stars of diff^i^rent alti- 

 tudes. Let us suppose that, with an instrument liable to flex- 

 ure, it is required to measure by both methods the meridional 

 distance of any two stars. The angular distance of the direct 

 images will (as we have already seen) be affected by the dif- 

 ference, or by the sum of two flexures, according as the stars 

 are placed on the same or on opposite sides of the zenith. In 

 viewing the reflected images, the instrument, receiving two new 

 positions, will be subject to two new flexures, by the sum or 

 difference of which (as it may happen) the angular distance of 

 the reflected images will be affected. 



The most probable supposition to be made concerning the 

 flexures is, that at equal inclinations with the horizon, above 

 and below it, they will be the same nearly both in direction 

 and degree, and therefore that the two images below the hori- 

 zon will approach by nearly the same quantity that the direct 

 images receded, or vice versa. With an instrument therefore 

 having such a system of flexures, the double altitude of each 

 star will be correctly ascertained ; but stars of different alti- 

 tudes will give different determinations (if the hoi'izontal point. 



From 



